I'm sorry to hear about the problems your wife is experiencing with her Nissan Juke. Sadly this is not an uncommon complaint (CVT gearbox failures are increasingly common on this car). You can see all of the reported problems for this generation of the Juke here: www.honestjohn.co.uk/carbycar/nissan/juke-2010/

If the vehicle has a full dealer stamped service history then I would expect them to make a 'goodwill contribution' on your behalf to Nissan UK. Otherwise, I think it would be better to get a second opinion from an independent garage. I would suggest taking the car to a member of: www.fedauto.co.uk/